2017/12/01 by Simon Pigeon, Karl Fogelmark, Bo Söderberg +2 · 3 citations
Chemistry · Mathematics · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Anomalous diffusion #Bravais lattice #Constant (computer programming) #Diffusion #Fick's laws of diffusion #Particle (ecology) #Particle dynamics #Stochastic processes and statistical mechanics #TRACER #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1088/1742-5468/aa9db3
published in Journal of Statistical Mechanics Theory and Experiment 2017(12), 123209 (Institute of Physics) · 28 pages with appendix, 5 figure. To appear in JSTAT
openalex publication_date 2017/12/01 · arxiv created 2017/12/13 · arxiv updated 2017/12/22 · openalex created_date 2017/12/22 · openalex updated_date 2026/08/05
Abstract In this study, inspired by the work of Nakazato and Kitahara (1980 Prog. Theor. Phys . 64 2261), we consider the theoretical problem of tracer particle diffusion in an environment of diffusing hardcore interacting crowder particles. The tracer particle has a different diffusion constant from the crowder particles. Based on a transformation of the generating function, we provide an exact formal expansion for the tracer particle probability density, valid for any lattice in the thermodynamic limit. By applying this formal solution to dynamics on a regular Bravais lattice we provide a closed form approximation for the tracer particle diffusion constant which extends the Nakazato and Kitahara results to include also b.c.c. and f.c.c. lattices. Finally, we compare our analytical results to simulations in two and three dimensions.